Turbulence regulation by stochastic zonal flows in dynamical models

A theory of turbulence reduction by zonal flows is presented in the interchange turbulence model. Zonal flows with a finite correlation time τZF are shown to lead to a significant reduction in particle transport and turbulence amplitude, with the scalings ⟪nυx⟫∝τDΩeff−1∝Ωeff−3∕2, ⟪n2⟫∝τD∝Ωeff−1∕2, and ⟪υx2⟫∝τDΩeff−2∝Ωeff−5∕2. Here, Ωeff=τZFΩrms2, τD=(τη∕Ωeff)1∕2, and τη are the effective shearing rate, effective decorrelation time, and diffusive turbulent scattering time, respectively. Compared to the transport of passive scalar fields [E. Kim and P. H. Diamond, Phys. Plasmas, 11, L77 (2004)], the reduction is much more severe due to the suppression of turbulent velocity. However, the overall transport and turbulence amplitude are still larger compared with the case of coherent shearing because shearing by random zonal flows with a finite correlation time is less efficient, with a longer decorrelation time τD than (τη∕Ω2)1∕3 in the case of coherent shearing.